78.8.8 problem 8

Internal problem ID [18206]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 11:38:20 AM
CAS classification : [_separable]

\begin{align*} x y^{\prime }+y&=x^{2} y^{\prime }+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(x*diff(y(x),x)+y(x)=x^2*diff(y(x),x)+y(x)^2,y(x), singsol=all)
 

\[ y = \frac {x -1}{c_{1} x -1} \]

✓ Solution by Mathematica

Time used: 0.521 (sec). Leaf size: 33

DSolve[x*D[y[x],x]+y[x]==x^2*D[y[x],x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1-x}{1+\left (-1+e^{c_1}\right ) x} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}